Yes but i'd still say if u have a degree from oxbridge u'd be better off, in terms of employement ofcourse...
On the general point of LSE applications it seems that law, economics, management, accountancy and international relations all have tough entry requirements and masses of applicants (those accepted will have far higher A Level grades than the standard offers).
However if you don't fancy this particular lottery, then take a look at some of the other courses. Any LSE undergrad degree with the word 'social' in front of it for instance seems to be much easier to get into, and when you study it there will be a lot less in the way of boring maths. There are far fewer applicants and the basic offer is much lower.
At the end of three years you'd still emerge with a qualification from a world famous place, and come to that the relevant department will almost certainly be a leader in its field. You won't be quite as employable as somebody with law or economics, but the grade of your degree may be higher because your course will probably be easier than things like econ. And you can pick up other qualifications later and many employers like recruiting generalists from a name university whom they can train themselves- on the other hand by then you may even want to become a sociologist or an anthropologist!